You should use 5" black stove pipe and a 6" Fields RC damper. See my installation photos in this post:5" up to 6" flu pipe
This concentric pipe install is what A-A recommends in their installation manual. It's especially suitable for high natural draft flues. The baro should go at the chimney thimble. You want the 5" pipe to have the minimum of bends. Eliminate true 90 degree turns and clean out tees. What you are trying to achieve is high stove pipe velocity, ideally laminar flow. When the combustion blower is running this will convey the fly ash to the chimney. There a large change in pressure will occur because the velocity flow goes from 5" to the large chimney area. The fly ash will fall out and drop to the bottom of the chimney. You clean this annually.
There is no need for the more expensive Fields type M in this application. The Type M is for applications requiring more sensitivity in automatic adjustment to flue gas velocity changes. This is not one of those applications, especially with the concentric flue pipe arrangement. You will need a baro to get it set. Depending on your particular chimney you may need to add more weight to the baro flapper. Most certainly ignore the factory engraved settings, they are completely wrong for this use. It's possible you may need to change the position of the two pipes, i.e. how far they fit into each other. They other thing you can do to adjust things is to trim away some of the inter pipe at the damper. This will allow more chimney draft through the damper door rather than going through the 5" pipe. My install has worked well for me.